The Pulp frontman, who presents his Sunday Service programme on BBC 6 Music, will uncover the stories of the "befuddled, the banged-up and the bedbound", said Radio 4.
In an interview with Radio Times, Cocker confirmed that the programme will air for half an hour from 11pm, starting on April 5.
He said that the new series would feature "various people telling stories in their own words about what they get up to at night".
Giving examples, he pointed to "a guy who likes to go up to his allotment and drink cans of beer while waiting to see if a badger comes out", and "people who gamble all night in slightly shady poker clubs".
The show will also include an interview with a man who had a row with his girlfriend and then ended up falling asleep in an empty building behind a washing machine. Waking in the morning, the man found that he had a new appreciation for "the sounds and echoes of dereliction".
Cocker said that he was attracted to doing the show, called Wireless Nights, because he has "always been quite nosy". He said that he hopes to become the "glue" that "makes these strands adhere together".
The singer, who won the rising star prize at the 2010 Sony Radio Academy Awards for his 6 Music show, has previously appeared on Radio 4 for Desert Island Discs in 2005, a guest editorship of Today in 2008 and documentary In Search of the Holy Whale last year.
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